Maths Skills for Chemistry (~20% of Marks)

Approximately 20% of the marks on each Edexcel GCSE Chemistry paper require mathematical skills. Across both papers, that is roughly 40 marks — enough to make the difference of several grades. This lesson covers every maths skill you need, with worked examples specific to Chemistry.

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The Maths Skills Tested

The Edexcel specification lists the following mathematical requirements:

Skill	Where It Appears in Chemistry
Arithmetic and numerical computation	Calculating Mr, moles, percentages
Handling data	Mean, range, identifying anomalies
Algebra	Rearranging formulae, substitution
Graphs	Plotting, reading values, calculating gradients
Geometry and measures	Unit conversions
Statistics	Mean calculations, understanding uncertainty

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Calculating Relative Formula Mass (Mr)

This is the foundation of almost every Chemistry calculation. You will use Mr in moles, concentration, percentage yield, and atom economy questions.

Method

1. Write out the formula
2. Look up each relative atomic mass (Ar) — these are given in the periodic table or in the question
3. Multiply each Ar by the number of atoms of that element
4. Add them all together

Worked Example

Calculate the Mr of calcium hydroxide, Ca(OH)₂.

• Ca: 40 × 1 = 40
• O: 16 × 2 = 32
• H: 1 × 2 = 2

Mr = 40 + 32 + 2 = 74

Worked Example (more complex)

Calculate the Mr of magnesium nitrate, Mg(NO₃)₂.

• Mg: 24 × 1 = 24
• N: 14 × 2 = 28 (the subscript 2 outside the bracket applies to everything inside)
• O: 16 × (3 × 2) = 96

Mr = 24 + 28 + 96 = 148

Exam tip: The most common Mr error is forgetting to multiply everything inside a bracket by the subscript outside it. Mg(NO₃)₂ has 2 nitrogen atoms and 6 oxygen atoms, not 1 nitrogen and 3 oxygens.

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Moles Calculations

The Triangle

The moles formula can be arranged three ways:

To Find	Formula
Moles	moles = mass ÷ Mr
Mass	mass = moles × Mr
Mr	Mr = mass ÷ moles

Worked Example: Reacting Masses

Question: What mass of carbon dioxide is produced when 10.0 g of calcium carbonate reacts with excess hydrochloric acid?

CaCO₃ + 2HCl → CaCl₂ + H₂O + CO₂

Step 1: Calculate moles of CaCO₃ Mr of CaCO₃ = 40 + 12 + (16 × 3) = 100 moles = 10.0 ÷ 100 = 0.10 mol

Step 2: Use the balanced equation to find moles of CO₂ From the equation: 1 mol CaCO₃ produces 1 mol CO₂ So 0.10 mol CaCO₃ produces 0.10 mol CO₂

Step 3: Calculate mass of CO₂ Mr of CO₂ = 12 + (16 × 2) = 44 mass = 0.10 × 44 = 4.4 g

Exam tip: Always use the balanced equation to find the mole ratio. This is the step most students skip, and it is where many errors occur.

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Concentration Calculations

There are two types of concentration in GCSE Chemistry:

Type	Formula	Units
Moles per volume	concentration = moles ÷ volume	mol/dm³
Mass per volume	concentration = mass ÷ volume	g/dm³

Converting Between the Two

concentration (g/dm³) = concentration (mol/dm³) × Mr

Worked Example

Question: A solution has a concentration of 0.50 mol/dm³. The solute is sodium chloride (NaCl, Mr = 58.5). What is the concentration in g/dm³?

concentration = 0.50 × 58.5 = 29.25 g/dm³

Worked Example

Question: 4.0 g of sodium hydroxide (NaOH, Mr = 40) is dissolved in 200 cm³ of water. Calculate the concentration in mol/dm³.

Step 1: Convert volume: 200 cm³ = 0.200 dm³ Step 2: Calculate moles: moles = 4.0 ÷ 40 = 0.10 mol Step 3: Calculate concentration: 0.10 ÷ 0.200 = 0.50 mol/dm³

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Percentage Yield Calculations

Formula

percentage yield = (actual yield ÷ theoretical yield) × 100

Why the Yield Is Never 100%

• Some product is lost during transfer between containers
• Some product is lost during filtration or evaporation
• The reaction may not go to completion
• Side reactions may occur

Worked Example

Question: A student expects to produce 12.0 g of magnesium oxide but actually obtains 9.6 g. Calculate the percentage yield.

percentage yield = (9.6 ÷ 12.0) × 100 = 80.0%

Exam tip: The percentage yield can never be more than 100%. If your answer is above 100%, you have made an error — check your working.

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Atom Economy Calculations

Formula

atom economy = (Mr of desired product ÷ sum of Mr of all products) × 100

Worked Example

Question: Hydrogen is produced by reacting zinc with sulfuric acid: Zn + H₂SO₄ → ZnSO₄ + H₂

Calculate the atom economy for producing hydrogen.

Mr of H₂ = 2 Mr of ZnSO₄ = 65 + 32 + (16 × 4) = 161 Sum of Mr of all products = 161 + 2 = 163

atom economy = (2 ÷ 163) × 100 = 1.2%

Exam tip: Low atom economy means the reaction is wasteful — most of the atoms end up in the unwanted product. High atom economy reactions (like addition reactions) are more sustainable.

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Bond Energy Calculations (Higher Tier)

Formula

Energy change = energy required to break bonds − energy released when bonds form

• If the answer is positive: the reaction is endothermic (takes in energy)
• If the answer is negative: the reaction is exothermic (releases energy)

Worked Example

Question: Calculate the energy change for the combustion of hydrogen: 2H₂ + O₂ → 2H₂O

Bond	Bond Energy (kJ/mol)
H–H	436
O=O	498
O–H	464

Bonds broken:

• 2 × H–H = 2 × 436 = 872 kJ
• 1 × O=O = 498 kJ
• Total energy to break bonds = 872 + 498 = 1370 kJ

Bonds formed:

• 4 × O–H = 4 × 464 = 1856 kJ (each water molecule has 2 O–H bonds, and there are 2 water molecules)

Energy change: 1370 − 1856 = −486 kJ

The reaction is exothermic (negative energy change).